Analysts at Panmure Gordon said the company was worth up to £4.5 billion — well in excess of the current upper valuation of £3.3 billion.

Investors can apply for up to £10,000-worth of shares using a debit card on the Government’s website. The flotation is expected to be oversubscribed, as were many of the sell-offs in the Eighties, meaning that many people may not receive the share allocation they request.

The minimum investment is £750, which would result in an instant profit of at least around £300 after the float, if analysts’ predictions are correct.

Anyone looking to buy more shares will have to download an application form and send it in by first-class post to make sure it arrives by the deadline of midnight Tuesday.

The popularity of the sale has kick-started a political row, with Labour claiming that it should be halted because the massive demand shows Royal Mail is undervalued.

Claims that the company is undervalued are good news for private investors and are likely to be even better news for City investors and hedge funds.

The close of the share offer Tuesday will be followed by a three-day period of “conditional trading” when City institutions can buy and sell the shares between each other.

The final price will be announced on Friday and shares in Royal Mail will be traded on the London Stock Exchange from Monday next week.

Labour said it was concerned that hedge funds and speculators would make millions before the shares are available to the public on the open market.

Alan Johnson, a former business secretary, told The Daily Telegraph: “There is a vast difference between pricing Royal Mail shares conservatively and undervaluing them by £1 billion. This is ripping off the taxpayer on an epic scale.”

Party sources suggested that Labour was looking at ways to use parliamentary procedures to delay the flotation and allow a rethink on the valuation.

Chuka Umunna, the shadow business secretary, said the float should be halted on the grounds that the taxpayer could get a better deal by waiting.

He added: “What they need to illustrate is they are going to get the best value for the taxpayer and increasingly what this is looking like is a massive bonanza for City speculators and a huge short-changing of the taxpayer at the same time.”

Part of Labour’s concern is that the Government’s City advisers have failed to take into account the £1 billion-plus property value of some of the Royal Mail’s sites, particularly the Mount Pleasant and Nine Elms delivery offices in London.

If Royal Mail decided to sell off the sites, any profits would be shared by the company’s shareholders, rather than wholly with the taxpayer.

Mr Umunna said: “Increasingly we are seeing more and more information coming out which would suggest that the taxpayer will be short-changed.”

One Cabinet minister dismissed the fears, telling The Daily Telegraph that if the shares were oversubscribed it was “a triumph”. The source said: “Labour have nowhere to go. Not only did they fail to privatise it, as they succumbed to union paymaster pressure, they left Royal Mail in a weak state.

“Their amendments during the Bill would have reduced its value and made it more difficult to sell.

“Labour are inconsistent and incoherent on Royal Mail: the only thing we know about Labour’s policy is that it led to post offices closing in their thousands.”

A Business Department spokesman said: “The Government is approaching the sale as a commercial shareholder and is seeking fair value for the shares and the best deal for taxpayers.

“This is a commercial transaction and government is following normal commercial practice in setting and publicising the share price and delivering value for the taxpayer.

“Final valuation will be determined by institutional investors through the book-building process, based on their assessment of Royal Mail, its strengths and potential for growth and returns.

“The value of Royal Mail will depend on a number of factors, notably the company’s ongoing financial performance, its future prospects and the level of investor interest. The Government will hold on to a stake in the business which could be sold at a future date.”